Related papers: Extremal clustering under moderate long range depe…
A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index…
The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…
Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The…
Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In…
We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
We study the asymptotic behaviour of stationary densities of one-dimensional random diffeomorphisms, at the boundaries of their support, which correspond to deterministic fixed points of extremal diffeomorphisms. In particular, we show how…
A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
We develop a novel characterization of extremal dependence between two cortical regions of the brain when its signals display extremely large amplitudes. We show that connectivity in the tails of the distribution reveals unique features of…
We develop an asymptotic theory for extremes in decomposable graphical models by presenting results applicable to a range of extremal dependence types. Specifically, we investigate the weak limit of the distribution of suitably normalised…
For a class of Gaussian stationary processes, we prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly growing linear boundary. The limit is a double exponential (Gumbel) distribution.
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…
The conditional extremes (CE) framework has proven useful for analysing the joint tail behaviour of random vectors. However, when applied across many locations or variables, it can be difficult to interpret or compare the resulting extremal…
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…
Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to…
We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values.
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained (see previous work by Bhamidi, van der Hofstad and van Leeuwaarden).…